The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Subresultants and Reduced Polynomial Remainder Sequences
Journal of the ACM (JACM)
On Euclid's Algorithm and the Computation of Polynomial Greatest Common Divisors
Journal of the ACM (JACM)
The Subresultant PRS Algorithm
ACM Transactions on Mathematical Software (TOMS)
Probabilistic algorithms for sparse polynomials
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
ACM '73 Proceedings of the ACM annual conference
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
GCDHEU: Heuristic polynomial GCD algorithm based on integer GCD computation
Journal of Symbolic Computation
On the multi-threaded computation of integral polynomial greatest common divisors
ISSAC '91 Proceedings of the 1991 international symposium on Symbolic and algebraic computation
Three new algorithms for multivariate polynomial GCD
Journal of Symbolic Computation
On computing greatest common divisors with polynomials given by black boxes for their evaluations
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
Evaluation of the heuristic polynomial GCD
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
On the design and implementation of Brown's algorithm over the integers and number fields
ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
Algorithms for the non-monic case of the sparse modular GCD algorithm
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
P-adic reconstruction of rational numbers
ACM SIGSAM Bulletin
An improved EZ-GCD algorithm for multivariate polynomials
Journal of Symbolic Computation
Computing multivariate approximate GCD based on Barnett's theorem
Proceedings of the 2009 conference on Symbolic numeric computation
A parallel algorithm to compute the greatest common divisor of sparse multivariate polynomials
ACM Communications in Computer Algebra
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An enhanced gcd algorithm based on the EZ-GCD algorithm is described. Implementational aspects are emphasized. It is generally faster and is particularly suited for computing gcd of sparse multivariate polynomials. The EEZ-GCD algorithm is characterized by the following features:(1) avoiding unlucky evaluations,(2) predetermining the correct leading coefficient of the desired gcd,(3) using the sparsity of the given polynomials to determine terms in the gcd and(4) direct methods for dealing with the "common divisor problem." The common divisor problem occurs when the gcd has a different common divisor with each of the cofactors. The EZ-GCD algorithm does a square-free decomposition in this case. It can be avoided resulting in increased speed. One method is to use parallel p-adic construction of more than two factors. Machine examples with timing data are included.